Every biologist is familiar with the remarkable discoveries of Morgan and his associates concerning the germ-cells of Drosophila. One of the most important of these discoveries is concerned with the phenomenon of linked inheritance. This kind of inheritance, while entirely conformable with Mendel's law, forms a very distinct and important class of cases whose existence has been brought to light since the rediscovery of the general law in 1900. Under the general law it is found that characters which behave as distinct units in heredity assort quite independently of each other. Thus if parents are crossed one of which possesses two characters, A and B, while the other lacks them, then the offspring of this cross will transmit A and B sometimes associated in the same gamete, sometimes in different gametes, the two events being under the laws of chance equally probable. But in linked inheritance, a phenomenon first made known to us through the work of Bateson and his associates in England, later more fully explored and explained by Morgan, A and B are not wholly independent of each other in transmission. If they enter a cross together, they have a tendency to stay together in later generations; and if they enter a cross separately, they have a tendency to remain apart in later generations. Morgan has suggested that what binds or links two characters together is the fact that their genes lie in the same body within the cell-nucleus. Such bodies he supposes are the chromosomes. The evidence for this conclusion is very strong. Morgan and his associates have demonstrated the existence in Drosophila of four groups of linked genes corresponding with the four pairs of chromosomes which the cell-nucleus of Drosophila contains. Morgan has further suggested (and has beyond doubt established the fact) that the genes within a linkage system have a very definite and constant relation to each other. He supposes their arrangement to be linear and in the group of genes most exhaustively studied, that of the 'sex chromosome' has represented them in a 'chromosome map, as shown in Diagram I. That the arrangement of the genes within a linkage system is strictly linear seems for a variety of reasons doubtful. It is doubtful, for example, whether an elaborate organic molecule ever has a simple string-like form. Let us, therefore, examine briefly the evidence for or against the idea of linear arrangement of the genes. It is supposed by Morgan that two genes lying in the same chromosome show close linkage if they lie close together, but less linkage if they lie farther apart, and that the farther apart they are the less will be their linkage. As a measure of the distance apart of two genes he takes the percentage of cross-overs between them. This term requires a word of explanation. If two genes, A and B, enter a cross in the same gamete and emerge from it in different gametes, one of them has evidently crossedover from the chromosome in which it lay to the mate of that chromosome (all chromosomes being paired prior to the formation of gametes). Likewise if the two genes, A and B, having entered a cross separately (being contributed by different parents), later emerge from the cross together, it is evident that one of them has again crossed-over so as to lie in the same chromosome as the other. The readiness with which cross-overs occur between two genes will on Morgan's hypothesis depend on their distance apart and the percentage of cross-overs between genes will be proportional to the distances between them. These assumptions have abundantly proved their utility as a working hypothesis, for it has been found possible, knowing what certain cross-over values are, to predict others with a fairly good degree of accuracy. = If the arrangement of the genes is strictly linear, so that A, B, C, etc., lie in a straight line, then it should be possible to infer the distance AC, if the distances AB and BC are known, since AC AB+ BC. But if the distance AC is less than the sum of AB and BC, then the arrangement can not be linear, since B will lie out of line with A and C. In reality it has been found that the distances experimentally determined between genes remote from each other are in general less than the distances calculated by summation of supposedly intermediate distances, and the discrepancy increases with increase in the number of known intermediate genes. To account for this discrepancy Morgan has adopted certain subsidiary hypotheses, of 'interference,' 'double crossing over,' etc., in accordance with which it is supposed that cross-overs between nearer genes interfere with or lessen the apparent amount of crossing-over with genes more remote. He therefore bases his chromosome map on summation of the shorter distances. This, however, leads to results which can be shown to be impossible. Morgan's map of the sex-chromosomes places five out of twenty-nine genes at distances between 55 and 66 from the zero end of the chromosome, where yellow is located. A moment's reflection will show these to be impossible re "Diagram I shows the relative positions of the genes of the sex-linked characters of Drosophila. One unit of distance corresponds to 1% of crossing-over." Morgan and Bridges, p. 23. lations, for a cross-over percentage greater than fifty is absurd. If A and B assort wholly independently, without any linkage whatever, just as they would in ordinary Mendelian inheritance where no linkage exists, crossovers and non-cross-overs will be equal, 50% each. Any cross-over value consistently less than 50% shows linkage. A cross-over value greater than fifty cannot exist. For there must be either linkage or no-linkage. But no-linkage means 50% cross-overs, and linkage means less than 50% crossovers. Hence a value greater than 50% cannot occur.1 As an alternative to the hypothesis of linear arrangement it is possible to suppose that the arrangement of the genes is not linear, that the nearer genes are not directly in line with the more remote ones. If the arrangement of the genes is not linear, what then is its character? This query led me to attempt graphic presentation of the relationships indicated by the data of Morgan and Bridges2 but finding this method unsatisfactory I resorted to reconstruction in three dimensions, which has proved very satisfactory. The data used consist of the experimentally determined cross-over percentages between twenty genes of the sex-chromosome of Drosophila, as given in Table 65 of Morgan and Bridges. The only hypothesis involved in the reconstruction is Morgan's fundamental one that distances between genes are proportional to cross-over percentages. The secondary hypothesis, that distant genes are really farther apart than indicated by the experimental data, is rejected for the reason already explained, that impossible relationship are thereby entailed. Taking the data, then, exactly as they stand, we find it possible to make a very complete and on the whole self-consistent reconstruction of the architecture of the sex-chromosome from the linkage relations of its genes. A small ring of wire is taken to represent the locus of a gene. Two genes are placed as far apart (in inches) as there are units in the cross-over percentage between them. Thus between yellow-body and white-eye there is shown by Morgan's data to be a cross-over value of 1.1%. Consequently the rings which represent these genes in the reconstruction are joined by a wire 1.1 inches long. Between white and vermilion the cross-over percentage is 30.5. Accordingly the connecting wire in this case is made 30.5 inches long. Proceeding in this way the reconstruction shown in figures 1 and 2 is obtained. It indicates an arrangement of the genes not by any means linear, but rather in the form of a roughly crescentic plate longer than it is wide, and wider than it is thick. It is shown in side view in figure 1, and in edge view in figure 2. That the arrangement of the genes can not by any possibility be linear is shown by two critical cases, the loci for bifid and abnormal. Bifid (Bi, figs. 1 and 2) is shown by a series of over 3,600 observations to be at a distance 5.5 from yellow. It is almost the same distance from white, viz., 5.3, as shown by 23,595 observations. Yet white and yellow are distant from each other only 1.1 units, as shown by 81,299 observations. Therefore bifid can lie neither above nor below yellow and white, in the line which joins them, but |